求系列 0.1, 0.11, 0.111, ... 的 N 项之和
给定一个正整数N 。找到系列的前N 项的总和-
0.1, 0.11, 0.111, 0.1111, ….till N terms
例子:
Input: N = 6
Output: 0.654321
Input: N = 1
Output: 0.1
方法:
1st term = 0.1
2nd term = 0.11
3rd term = 0.111
4th term = 0.1111
.
.
Nth term = 1/9(1 – (1/10) ^ N)
该序列是通过使用以下模式形成的。对于任何值 N-
推导:
以下一系列步骤可用于推导公式以找到 N 项的总和 -
The series 0.1, 0.11, 0.111, …till N terms can be written as
-(1)
The series is in G.P. with
First term a = 0.1 = 10-1
Common Ratio r = 10-1
Sum of G.P. for r<1 can be expressed as-
Substituting the values of a and r in the equation-
-(2)
Substituting the eqution (2) in (1), we get-
插图:
Input: N = 6
Output: 0.654321
Explanation:
以下是上述方法的实现 -
C++
// C++ program to implement
// the above approach
#include
using namespace std;
// Function to return sum of
// N term of the series
double findSum(int N)
{
int a = pow(10, N);
return (double)(N * 9 * a - a + 1)
/ (81 * a);
}
// Driver Code
int main()
{
int N = 6;
cout << findSum(N);
}
Java
// Java program for the above approach
import java.io.*;
import java.lang.*;
import java.util.*;
class GFG {
// Function to return sum of
// N term of the series
static double findSum(double N)
{
double a = Math.pow(10, N);
return (double)(N * 9 * a - a + 1)
/ (81 * a);
}
// Driver Code
public static void main (String[] args) {
double N = 6;
System.out.print(findSum(N));
}
}
// This code is contributed by hrithikgarg03188.
Python3
# Python 3 program for the above approach
# Function to return sum of
# N term of the series
def findSum(N):
a = pow(10, N)
return (N * 9 * a - a + 1) / (81 * a)
# Driver Code
if __name__ == "__main__":
# Value of N
N = 6
print(findSum(N))
# This code is contributed by Abhishek Thakur.
C#
// C# program to implement
// the above approach
using System;
class GFG
{
// Function to return sum of
// N term of the series
static double findSum(int N)
{
int a = (int)Math.Pow(10, N);
return (double)(N * 9 * a - a + 1)
/ (81 * a);
}
// Driver Code
public static void Main()
{
int N = 6;
Console.Write(findSum(N));
}
}
// This code is contributed by Samim Hossain Mondal.
Javascript
0.654321
时间复杂度: O(1)
辅助空间: O(1)